RE: [tuning] Re: Part 3: Definition Question for Paul Erlich: "Tr ue" Interval

Jacky Ligon wrote,

>am I correct to assume that
>there is a sort of gradient scale of tonal gravity for each interval
>in terms of where it falls in integer size?

Yes.

>If true, then the
>harmonic series would provide the order of gravitational pull: 1/1,
>2/1, 3/1, 4/1, 5/1 etc...right - wrong?

It actually seems like the denominator, not the numerator, of the ratio
(when expressed as you did, with the numerator larger), is a good measure of
how strong the field of attraction is. The lower the denominator, the
stronger the field.

Dan wrote,

>If I'm reading this all correctly, then I would think that Paul would
>argue that it's the consistent occurrences of minima across the two
>variables of N (given that you start with a high enough N in the first
>place) and s that are most pertinent, rather than something like a
>cleanly ordered trough depth... but I'll digress and leave the cleanup
>job to Paul!

Well, for the very simplest ratios, the denominator rule seems to work well;
it is s that is a limiting factor to how far you can extend this rule to
more complex ratios.

> [Jacky Ligon]
>
> > If true, then the harmonic series would provide the order
> > of gravitational pull: 1/1, 2/1, 3/1, 4/1, 5/1 etc...
> > right - wrong?
>

> [Paul Erlich]
>http://www.egroups.com/message/tuning/11950
>
> It actually seems like the denominator, not the numerator, of
> the ratio (when expressed as you did, with the numerator larger),
> is a good measure of how strong the field of attraction is. The
> lower the denominator, the stronger the field.

This smells familiar... didn't we discuss this a while back,
and come to the conclusion that it was the smaller ratio term,
regardless of whether numerator or denominator, that determines FoA?

-monz
http://www.ixpres.com/interval/monzo/homepage.html

Monz wrote,

>This smells familiar... didn't we discuss this a while back,
>and come to the conclusion that it was the smaller ratio term,
>regardless of whether numerator or denominator, that determines FoA?

When you use a Farey series as your "ratio universe", this is true, and I
posted a proof that is related to this fact. If you use another series,
however, you might get some other rule involving both terms in the ratio . .
. The nice thing about the Farey series is that it's "all intervals present
in the harmonic series up to the Nth partial", which makes it easy to
justify as a universe of relevant ratios . . .